There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
The letters of the word ABACUS have been arranged in the shape of a
triangle. How many different ways can you find to read the word
ABACUS from this triangular pattern?
A few extra challenges set by some young NRICH members.
Rather than using the numbers 1-9, this sudoku uses the nine
different letters used to make the words "Advent Calendar".
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
Countries from across the world competed in a sports tournament. Can you devise an efficient strategy to work out the order in which they finished?
A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
A package contains a set of resources designed to develop
students’ mathematical thinking. This package places a
particular emphasis on “being systematic” and is
designed to meet. . . .
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.
If you take a three by three square on a 1-10 addition square and
multiply the diagonally opposite numbers together, what is the
difference between these products. Why?
You have been given nine weights, one of which is slightly heavier
than the rest. Can you work out which weight is heavier in just two
weighings of the balance?
A student in a maths class was trying to get some information from
her teacher. She was given some clues and then the teacher ended by
saying, "Well, how old are they?"
Given the products of adjacent cells, can you complete this Sudoku?
A man has 5 coins in his pocket. Given the clues, can you work out
what the coins are?
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.
This package contains a collection of problems from the NRICH
website that could be suitable for students who have a good
understanding of Factors and Multiples and who feel ready to take
on some. . . .
This challenge extends the Plants investigation so now four or more children are involved.
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
Mr McGregor has a magic potting shed. Overnight, the number of
plants in it doubles. He'd like to put the same number of plants in
each of three gardens, planting one garden each day. Can he do it?
In this matching game, you have to decide how long different events take.
What could the half time scores have been in these Olympic hockey
Ben passed a third of his counters to Jack, Jack passed a quarter
of his counters to Emma and Emma passed a fifth of her counters to
Ben. After this they all had the same number of counters.
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Can you find which shapes you need to put into the grid to make the
totals at the end of each row and the bottom of each column?
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
This Sudoku, based on differences. Using the one clue number can you find the solution?
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.
Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
Four friends must cross a bridge. How can they all cross it in just 17 minutes?
How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?
This challenge is to design different step arrangements, which must
go along a distance of 6 on the steps and must end up at 6 high.
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
On a digital clock showing 24 hour time, over a whole day, how many
times does a 5 appear? Is it the same number for a 12 hour clock
over a whole day?
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2
litres. Find a way to pour 9 litres of drink from one jug to
another until you are left with exactly 3 litres in three of the
When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?